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Simplifying 8x2 + 20x + -100 = 6x2 + 5x + -21 Reorder the terms: -100 + 20x + 8x2 = 6x2 + 5x + -21 Reorder the terms: -100 + 20x + 8x2 = -21 + 5x + 6x2 Solving -100 + 20x + 8x2 = -21 + 5x + 6x2 Solving for variable 'x'. Reorder the terms: -100 + 21 + 20x + -5x + 8x2 + -6x2 = -21 + 5x + 6x2 + 21 + -5x + -6x2 Combine like terms: -100 + 21 = -79 -79 + 20x + -5x + 8x2 + -6x2 = -21 + 5x + 6x2 + 21 + -5x + -6x2 Combine like terms: 20x + -5x = 15x -79 + 15x + 8x2 + -6x2 = -21 + 5x + 6x2 + 21 + -5x + -6x2 Combine like terms: 8x2 + -6x2 = 2x2 -79 + 15x + 2x2 = -21 + 5x + 6x2 + 21 + -5x + -6x2 Reorder the terms: -79 + 15x + 2x2 = -21 + 21 + 5x + -5x + 6x2 + -6x2 Combine like terms: -21 + 21 = 0 -79 + 15x + 2x2 = 0 + 5x + -5x + 6x2 + -6x2 -79 + 15x + 2x2 = 5x + -5x + 6x2 + -6x2 Combine like terms: 5x + -5x = 0 -79 + 15x + 2x2 = 0 + 6x2 + -6x2 -79 + 15x + 2x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -79 + 15x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -39.5 + 7.5x + x2 = 0 Move the constant term to the right: Add '39.5' to each side of the equation. -39.5 + 7.5x + 39.5 + x2 = 0 + 39.5 Reorder the terms: -39.5 + 39.5 + 7.5x + x2 = 0 + 39.5 Combine like terms: -39.5 + 39.5 = 0.0 0.0 + 7.5x + x2 = 0 + 39.5 7.5x + x2 = 0 + 39.5 Combine like terms: 0 + 39.5 = 39.5 7.5x + x2 = 39.5 The x term is 7.5x. Take half its coefficient (3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. 7.5x + 14.0625 + x2 = 39.5 + 14.0625 Reorder the terms: 14.0625 + 7.5x + x2 = 39.5 + 14.0625 Combine like terms: 39.5 + 14.0625 = 53.5625 14.0625 + 7.5x + x2 = 53.5625 Factor a perfect square on the left side: (x + 3.75)(x + 3.75) = 53.5625 Calculate the square root of the right side: 7.318640584 Break this problem into two subproblems by setting (x + 3.75) equal to 7.318640584 and -7.318640584.Subproblem 1
x + 3.75 = 7.318640584 Simplifying x + 3.75 = 7.318640584 Reorder the terms: 3.75 + x = 7.318640584 Solving 3.75 + x = 7.318640584 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = 7.318640584 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = 7.318640584 + -3.75 x = 7.318640584 + -3.75 Combine like terms: 7.318640584 + -3.75 = 3.568640584 x = 3.568640584 Simplifying x = 3.568640584Subproblem 2
x + 3.75 = -7.318640584 Simplifying x + 3.75 = -7.318640584 Reorder the terms: 3.75 + x = -7.318640584 Solving 3.75 + x = -7.318640584 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = -7.318640584 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = -7.318640584 + -3.75 x = -7.318640584 + -3.75 Combine like terms: -7.318640584 + -3.75 = -11.068640584 x = -11.068640584 Simplifying x = -11.068640584Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.568640584, -11.068640584}
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